Permanently installed Terrestrial Laser Scanner and Synthetic Aperture Radar data: evaluation of correlation factor through time series analysis on coastal area under varying environmental conditions

In the past years, our knowledge of coastal environments has been enriched by remotely 1 sensed data. However, to successfully extract information from a combination of different sensors 2 systems, it should be understood how these interact with the common coastal environment. In this 3 research we co-analyze two sensor systems: Terrestrial Laser Scanning (TLS) and satellite based 4 Synthetic Aperture Radar (SAR). TLS shows large potential for examining coastal processes thanks to 5 the possibility to retrieve repeated, accurate and dense topographic information in a rapid and non6 invasive manner. However, TLS presents some limits due to its high economic costs and limited field 7 of view. SAR systems are among the most used active remote sensor system for Earth Observation. 8 Despite their relatively low resolution, SAR systems provide the ability to monitor and map coastal 9 areas with complete, repeated and frequent coverage, penetrating through clouds and providing 10 all weather monitoring. Moreover, Sentinel-1 SAR images are freely available. The availability of a 11 permanently installed TLS system (PLS, Permanent Laser Scanner) allows us, to extensively compare 12 Sentinel-1 SAR data and topographic laser scans during different conditions on a sandy beach. PLS 13 data are compared with simultaneous Sentinel-1 SAR images in order to investigate the combined 14 use of PLS and SAR in coastal environments. The purpose of this comparison is the investigation 15 of a possible relation between PLS and SAR data: knowing their relation, SAR dataset could be 16 correlated to beaches characteristics. Meteorological and surface roughness have also been taken 17 into consideration in the evaluation of the correlation between PLS and SAR data. The permanently 18 installed laser scanner for the present study is located in Noordwijk (the Netherlands). A generally 19 positive but low correlation exists between the two variables. When considering weather phenomena, 20 their correlation increases and shows a dependence on wind directions and speed. The correlation 21 with the surface roughness, evaluated in terms of root-mean squared height, also depends on specific 22 wind speed and directions. 23


Introduction
During the last years, Terrestrial Laser Scanning (TLS) has been successfully exploited 26 in many applications thanks to its ability to capture both geometric information and to 27 register backscatterd laser intensity of the scanned objects. Among its applications, forestry 28 [1][2][3], river systems [4,5] and geomorphology [6,7] have been investigated. In the past 29 years, the knowledge on coastal environments has been enriched by information provided 30 by TLS systems which show significant potential for examining coastal processes [8][9][10]. 31 Among the coastal applications, TLS have been used in order to generate Digital Elevation 32 Models (DEM) and to evaluate accurate volumetric changes on beaches, dunes and cliffs, 33 [11]: thanks to the high density of the point clouds with high accuracy/precision, TLSs 34 are suitable for the detailed DEM mapping of features on hundreds of meters of the beach- 35 dunes systems [12]. Several studies have also demonstrated the potential of estimating 36 other beach features as the surface moisture using both short and long-range TLS [10, 37 13-16]. 38 TLSs have the advantage over other surveying techniques that they can provide 39 accurate and dense information in a rapid and non-invasive manner [17]. Moreover, they 40 can scan a beach repeatedly without correction for changes in illumination because it works 41 as an active sensor [13][14][15]18]. On the other hand, TLS has some disadvantages when used 42 in large environments as coastal areas, such as a limited field of view, high economic cost, 43 heavy material (difficulties for portability), longer measurement time, problems with little 44 misalignments requiring calibration of reference points, and sight shadowing [19]. 45 Space-born remote sensing provides a unique ability to monitor and map coastal 46 areas with complete, repeated, and frequent coverage of the Earth's surface, [20]. In 47 particular active microwave remote sensing systems, despite their lower resolution, can 48 penetrate through clouds and provide continuous and all-weather monitoring. This allows 49 for more reliable and consistent sand monitoring. Synthetic Aperture Radar (SAR) is the 50 most common active remote sensing system for Earth observation [21]. In recent years, 51 many studies demonstrated the advantage of using SAR for the estimation of soil surface 52 characteristics, such as surface roughness and soil moisture [22,23]. Different sensor 53 configurations, in terms of wavelength, polarization, and incidence angle, allow for the 54 discrimination of various soil parameters, such as surface roughness, soil dielectric constant, 55 and vegetation cover [24,25]. 56 The combined use of TLS and SAR systems has been poorly investigated, and literature 57 is mostly limited to forest fire [26,27] and vegetation [28] estimation. In this work we present 58 new results from a Permanent terrestrial Laser Scanner (PLS) [29] based investigation on 59 beach environments. Both geometric information and backscatter laser intensity have been 60 collected from a permanently installed laser scanning device, a Riegl VZ-2000 [30]. The 61 PLS results are compared with simultaneous Sentinel-1 Synthetic Aperture Radar (SAR) 62 images [31] in order to investigate, for the first time, the synchronous use of PLS and radar 63 in beach environments. The purpose of this comparison is showing a possible relation 64 between PLS and SAR data: knowing this relation, SAR data could be correlated to beaches 65 characteristics assessable by PLS. 66 Several studies showed that remote sensing data on coastal environments is affected 67 by variables such as wind condition and surface roughness. This has been shown indepen-68 dently for both PLS [10,15,16] and SAR data where the backscattering behaviour depends 69 on the roughness in relation to the wavelength [32,33] and is affected by wind speed and 70 direction [34]. Therefore, notably meteorological conditions, in terms of wind speed and 71 direction and rain, and surface roughness, will be taken into consideration in the evaluation 72 of the correlation between PLS and SAR data.

73
The range for which roughness should be quantified depends on the application. 74 In [35], Lane states that roughness, as a component of topography, must be dealt with 75 implicitly at the scale of inquiry: depending on the specific range of scales, there is a 76 diversity in characterizing and defining the surface roughness. Higher-order roughness 77 representing elevation variations in the field ( [36]) has been considered in this work.

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Methods for soil roughness assessment involve different strategies, using both contact 79 and non-contact devices.

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TLS has been investigated as a technique for two-dimensional sampling of soil heights 81 able to detect elevation differences at mm range with relatively small effort, despite the high 82 equipment costs [37][38][39]. Assessment of surface roughness is one of the most challenging 83 applications of TLSs [40].

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One of the most common parameters applied for surface roughness quantification is 85 the standard deviation in vertical direction from a single mean value (Root-Mean Squared 86 Height, RMSH). Variations in height at different scales affect this index, therefore RMSH values are 88 commonly derived on a previously detrended surface in order to remove the effect of larger 89 scale roughness patterns as slope or curvature and to separate multi-scale effects [41,42].

90
In terms of roughness influence on the correlation between SAR and TLS systems, the 91 focus of this paper is to evaluate the effect of the roughness at a decimeter scale resolution 92 on the PLS system and, for the first time, its contribution to the relation between PLS and 93 SAR data. Roughness patterns at different scales were analyzed by RMSH using sliding 94 windows.

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After evaluating the RMSH index and considering different weather conditions in 96 terms of wind speed and direction, their contribution has been considered for evaluating to 97 what extent these variables affect the correlation between PLS and SAR dataset.

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The paper is structured as follows: in Section 2, the study area, the weather data 99 and the PLS and SAR data sets are presented; in Section 3, the data processing and the 100 roughness evaluation are presented and the methodology used to compare PLS and SAR 101 data is showed; in Section 4, the correlation between SAR and PLS on the study area is 102 presented, followed by the evaluation of the weather and roughness influence. Sections 5 103 and 6 show the Discussion and Conclusion of the present work.

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In this section, the study area and the used weather dataset are described, followed by 106 the presentation of the TLS and SAR data set.

Weather dataset 118
Several meteorological stations monitor the Dutch coast continuously providing de-119 tailed variables. Professional weather station data guarantee controlled information but 120 there are no data available close to the study area; therefore in the present study, as a 121 compromise, amateur weather station data have been used. These are less controlled 122 compared to professional weather station data, but available in the area of interest. For 123 the present study, information regarding wind speed and direction and precipitation at 124 the time of the satellite pass were collected. All the weather data used in this study are 125 local information collected at the moment of the satellite pass. Instantaneous values for 126 both wind speed and direction have been used, whilst for the rain the precipitation accu-127 mulation, which is the sum of precipitation over a certain period of time, has been used. 128 In particular, the precipitation accumulation over the past 1 hour before the satellite pass 129 has been considered. Three amateur weather stations were selected, since they provide the 130 type of data and the temporal sampling required. The meteorological stations are located 131 in Noordwijk (52.25°N, 4.43°E), Katwijk (N 52.19°N, 4.41°E) and Scheveningen (52.11°N, 132 4.29°E), all close to beach areas and close to the area of interest (respectively 1 km, 5 km 133 and 15 km). The weather stations in Noordwijk and Scheveningen have high correlation 134 coefficients with each other concerning the wind and rain variables. The wind data set 135 of station Noordwijk during the two years is not as complete as station Scheveningen, 136 therefore it has been discarded. The data set of the station Katwijk has been discarded since 137 the anemometers -devices used for measuring wind speed and direction -are located next 138 to a building or a wall, therefore their correlation with the two other stations was poor. The 139 values of the station Scheveningen have been therefore selected for the present analysis 140 (https://wow.knmi.nl/#919666001s). 141 Figure 3 shows the scatter of the collected wind speed relatively to the wind direction 142 at the moment of the satellite pass for the selected days of the stack. In the figure, each red 143 dot represents the instantaneous wind value (speed and direction) acquired simultaneously 144 to the Sentinel-1 pass over the study area for the entire stack. Considering the orientation 145 of the coastline, onshore wind occurs for direction ranging −30°and 150°.  The data is acquired on the same days and at the same time of the Sentinel-1 pass over 150 the study area. The laser scanner is scanning with 0.03°angular resolution (referred to as 151 low resolution -LR -in the following) and at a wavelength of 1550 nm. The study area 152 is at about 250 m range distance and the range accuracy (at 150 m range) equals 0.008 m, 153 according to the specifications [43]. With a slight surface slope of 1°towards the sea and 154 away from the laser scanner, the incidence angle is about 77°on average. The area contains 155 just under 30 000 points, resulting in a point density of about 10 points per m 2 . Because of 156 the relatively large incidence angle and range, the footprint in this area is about 0.066 m 2 157 with an ellipse shape of 0.3 m diameter on the long side. In the present work, the intensity 158 value is considered for the analysis. The intensity value is normalized with respect to a 159 reference level for each single point, therefore the intensity data is dimensionless [44]. The 160 output have been calibrated to allow the scan data to be range-independent [45]. Sentinel-1 is a constellation of two Sun-synchronous dawn/dusk orbiting (orbit height: 163 693 km, platform velocity: about 7.6 km/s) satellites [46], Sentinel-1A and Sentinel-1B, 164 which carry a C-band (operating at a wavelength of about 5 cm wavelenght) SAR sensor. 165 The repeat cycle of the Sentinel-1 constellation is 12 days for the single satellites and six 166 days for the two satellites together. Images at different polarizations and resolutions are 167 collected and free accessible from the Copernicus data hub [47]. 168 For the present study, Sentinel-1 data collected from Google Earth Engine have been 169 used after further processing steps. A single orbit (DSC37, parallel to the Dutch coastline) 170 has been selected. All the available Sentinel-1 images from the orbit DSC37 acquired 171 from 19/8/2019 to 22/4/2021 were downloaded (88 images). In Figure 4 the averaged 172 images in VV and VH polarization during the period of interest are showed. Regarding 173 the polarisation effect, it is well known that HH is more sensitive to surface scattering and 174 VH to volume scattering, and VV a combination of the two. VH backscatter is therefore 175 often used for the retrieval of crop parameters, and HH, ground parameters [48]. Sentinel-1 176 mission only provides data in VV and VH polarization. Sentinel-1 imagery in Earth Engine consists of Level-1 Ground Range Detected (GRD). 178 GRD are focused SAR data that have been detected, multi-looked and projected to ground 179 range using an Earth ellipsoid model. The SAR images used in the current study are 180 Interferometric Wide (IW) acquisition mode with 20 × 12 m spatial resolution (range 181 × azimut), dual polarization (VV + VH) and GRD product type. Within this collection, 182 all products have been already preprocessed using the European Space Agency's (ESA) 183 Step 1: Apply orbit file; Step 2: GRD border noise removal; 187

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Once created the stack of images for the area and period of interest, three further steps 191 have been performed: Step 6: Normalization of the backscatter coefficients, performed by using a dedicated 193 algorithm. The backscatter of a specific area with a small incidence angle return higher 194 backscatter values than the data of the same area acquired with a higher incidence 195 angle [50];

•
Step 7: Cosine correction. It is the most widely used incidence angle correction 197 technique [33]; Step 8: Noise correction. The images of the Sentinel-1 stack have been cropped 199 including not only the study site but a bigger area also including part of a city in 200 order to perform a noise correction. The pixels with the lowest variability have been 201 evaluated and selected and all the SAR images have been calibrated relatively to the 202 low variability area.

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In the present Section, the processing applied to the PLS data in terms of detrending is 205 shown and the methodology to evaluate the roughness index (RMSH) is presented. RMSH 206 is the most common parameter applied in recent studies for quantifying surface roughness 207 [51]. The index is calculated for a regular raster dataset of n × m pixel values. After data collection with the Riegl VZ-2000 laser scanner, the individual point clouds 210 are transformed into 3D point clouds in compressed laz-format in a local coordinate system 211 with the projected location of the laser scanner to elevation zero (NAP) as origin. This step is 212 done, in order to obtain positive elevation (NAP) instead of negative values, with respect to 213 the location of the laser scanner at 55 m height. The point clouds are recorded from a fixed 214 location and are therefore already coarsely co-registered (in the order of several centimeters). 215 Fine alignment or geo-location was not deemed necessary for the further analysis for this 216 study. The selected areas of interest are cut out using their x-and y-coordinates and filtered 217 for outliers, i.e., points which are outside of the expected elevation range (mean elevation 218 of the area with a margin of a few decimeter) for the respective areas. Then a plane is 219 fit through the points representing the selected area using principal component analysis 220 (PCA). With the help of the fitted plane, the slope is calculated and removed from the 221 elevation values of the respective areas, in order to enable the determination of surface 222 roughness, [41]. 223

RMSH evaluation 224
Surface roughness is reflected by the spatial heterogeneity of elevation values at a 225 pre-defined scale and its quantification depends on the dimensionality and resolution of 226 the data, as well as on the desired expressiveness of the index [51]. Considering that the 227 PLS provides about 10 cm point spacing at the study area, the roughness scale considered 228 in the present work is of the order of magnitude of few decimeters. This scale is the same 229 order of magnitude of the wavelength of the Sentinel-1 C band images used. RMSH is 230 evaluated from a previously detrended surface [41] in order to separate multi-scale effects, 231 with the remaining random roughness representing spatial variations [40,51].

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Considering that beach topography is highly heterogeneous in space, a local adapta-233 tion of the RMSH, the locRMSH (local RMSH) index has been applied in the present work. 234 A sliding window calculates the local variations in random roughness. The choice of an 235 appropriate window size is crucial for capturing different surface patterns [51]. The local 236 RMSH is obtained by the following equation [52]: with:

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• N the number of points in each cell;

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• z n , the z-value at the n-th points in the window;

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In the analysis of the present work, the local adaptation of the RMSH will be used. It 242 will be referred to it as RMSH. The selected area was scanned with the above specifications continuously during 246 two years. To investigate the effect of the relatively low resolution (LR) of this data set on 247 the RMSH evaluation, the same area was scanned with higher resolution (HR) and these 248 data have been compared to the LR data acquired one hour later in order to define the 249 window cell size for the locRMSH estimation. The same laser scanner with 0.015°angular 250 spacing was used on two occasions to acquire a scan of the same area resulting in a point 251 density of about 43 points/m 2 and the same footprint size (see Table 1). This leads to more 252 overlapping footprints.  When considering LR point clouds, the disadvantage of using a window size smaller than 1 m is the low number of points per pixel (less than 11) and that the mean ratio between HR and LR is high, especially when considering a 0.5 m cell. Figure 5 and Figure 6 show, for one of the two considered days of analysis, the value of the local RMSH [m] evaluated in each window cell, measuring 1 m and 5 m respectively, to give an indication of the order of magnitude of RMSH on the sandy area considered. Figure 7 shows the RMSH median relative difference between HR and LR images when considering different window size, for window size moving from 0.5 m to 12 m. This parameter has been computed as follows: for each pixel the relative difference between the locRMSH computed by using the HR image (locRMSH HR ) and the one computed with LR image (locRMSH LR ), indicated by the symbol ε RMSH has been evaluated with the equation: Then the median value of ε RMSH has been computed. So Figure 7 shows the median value 254 of ε RMSH as a function of the windows size for two point clouds, acquired in August 2019. 255 Whilst a significant difference (35%) exists for small window size (0.5 m), this difference 256 is almost halved for 1 m cells and converges for window cells ≥4 m, where the difference 257 is about 2%. Therefore, the dimension of the SAR pixels (12 m x 20 m) has been used as a 258 RMSH window cell size in the present study, with reduced influence of the laser scanner 259 resolution.

PLS and SAR comparison 261
A total of 12 SAR pixels covers the study area as showed in Figure 2. All the presented 262 analysis have been conducted for these 12 pixels. For this reason, considered PLS intensity 263 values of points included in each pixel have been averaged. A correlation factor has been 264 evaluated for each pixel of the study area between SAR backscatter and PLS intensity, 265 averaged over time. Similar correlation factors have been retrieved when considering SAR 266 VV and VH polarization in all the performed analysis. Therefore it has been decided to 267 show in the rest of the present study only the results obtained with VV polarization.

268
In order to further investigate the correlation between SAR backscatter and PLS 269 intensity, other variables which might affect the signal (both PLS and SAR) have been taken 270 into consideration. For this purpose we consider wind speed and direction at the moment 271 of the satellite pass and of the PLS scan of the beach. The wind speed has been considered 272 separately for a first analysis: all the wind speeds values have been divided into three 273 categories: low wind (<4 m/s), medium wind (4.1 − 8m/s), high wind (>8 m/s). The 274 correlation factor between PLS intensity and SAR backscatter data set has been evaluated 275 now for each pixel in the three cases of low, medium and high wind speed respectively.

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In this Section, we present the results of the present work in terms of correlation 278 between SAR backscatter and PLS intensity, see Section 4.1. The influence of weather 279 phenomena -in terms of wind conditions -and of the surface roughness on the PLS 280 intensity and on the correlation between PLS intensity and SAR backscatter is further 281 analysed in Section 4.2 and 4.3 respectively. The correlation factor between PLS intensity and SAR backscatter (VV polarization) 284 evaluated for each pixel of the study area is shown in Figure 8: a generally positive but 285 low correlation between the two variables in each pixel exists. Wind speed and direction 286 at the moment of the satellite pass and of the PLS scan of the beach have been considered 287 to further investigate the correlation between SAR and PLS signals. The correlation factor 288 between PLS intensity and SAR backscatter (VV polarization) data has been evaluated now 289 for each pixel in the three cases of low, medium and high wind speed respectively (see 290 Figure 9). Compared to the previous analysis, the correlation between SAR and PLS data in 291 the separate categories is now always higher and positive for each pixel when considering 292 low or medium wind (up to 0.5 correlation factor). For high wind speed, the correlation 293 becomes lower and irregular, both positive and negative depending on the considered pixel. 294 To further define the correlation values, also the wind directions have been considered. The 295 correlation factor has been evaluated for different sectors corresponding to different wind 296 directions: each sector ranges 90°(see Figure 10). In Figure 10, each sector represents a 297 90°wind direction section and each of the 12 rings represents a row of pixel starting from 298 pixel 1, which is located on the sea-side (inner ring) and moving towards pixel 12 (external 299 ring), which is located on the city-side of the study area. It is noticed that the correlation 300 has a interesting dependence on the wind direction and different directions show different 301 correlations. In particular when the wind direction ranges 90°-270°, several pixels show 302 positive correlation of up to 0.6. For offshore wind (direction ranging between 210°and 303 360°), most of the pixels have negative correlation up to 0.4. Most of the sectors have similar 304 range of colors, meaning that the 12 pixels of the study area present similar correlation on 305 equal wind direction conditions.  . Correlation factor (colorbar) between PLS intensity and SAR backscatter evaluated for different overlapping sectors ranging 90°wind directions. In the figure, each sector represents a 90°w ind direction section and each of the 12 rings represents a row of pixel starting from pixel 1, which is located on the sea-side (inner ring) and moving towards pixel 12 (external ring), which is located on the city-side of the study area. The dotted black line represents the orientation of the shore line in Noordwijk. mulation precipitation bigger than 0 mm/h. These days were considered not sufficient for 312 the statistic analysis. Therefore only analysis on the influence of wind has been performed. 313 At first, the wind speed has been considered. Figure 11 shows the correlation factor 314 between PLS intensity and wind speed for low, medium and high wind speed condition, 315 compare Section 3.3. For low and medium wind, each pixel shows that the PLS intensity 316 decreases with increasing wind. For high wind speed, the correlation turns positive and 317 ranges for each pixel between 0.6 and 0.8. This change of sign in the correlation factor 318 between PLS signal and high wind speed condition could explain the lack of correlation 319 between PLS and SAR data, as shown in Figure 9. The wind direction has also been 320 considered and the correlation factor between PLS intensity and SAR backscatter has been 321 evaluated for each pixel and for each wind direction section (See Figure 12). As in the 322 previous section, the correlation factor has been evaluated for different overlapping sectors 323 ranging 90°wind directions. In the figure, each sector represents a 90°wind direction 324 section and each of the 12 rings represent a row of pixel starting from pixel 1, which is 325 located on the sea-side (inner ring) and moving towards pixel 12 (external ring), which 326 is located on the city-side of the study area. Again, certain directions show different 327 correlation: in particular, the correlation factor between PLS and wind speed is negative 328 for almost all pixels (up to 0.5) for wind directions ranging between 90°and 300°(mostly 329 onshore wind), whilst a positive correlation exists (up to 0.5) for mostly offshore wind 330 (directions ranging 210°and 360°). The roughness variable and to what extent it affects both PLS intensity and SAR signal 333 has been analyzed by comparing RMSH index with TLS and SAR data set respectively. As 334 mentioned in Section 3.2, the RMSH index has been used as an indication of the roughness 335 of the soil. The index has been locally evaluated for each pixel. As a first step, the correlation 336 between the roughness and the wind has been evaluated (See Figure 13). As explained 337 in Section 3.3, the correlation factor has been evaluated separately for low, medium and 338 high wind speed. For low wind speed condition, the correlation with RMSH is negative 339 Correlation factor (colorbar) between PLS intensity and wind direction evaluated for different overlapping sectors ranging 90°wind directions. In the figure, each sector represents a 90°w ind direction section and each of the 12 rings represent a row of pixels starting from pixel 1, which is located on the sea-side (inner ring) and moving towards pixel 12 (external ring), which is located on the city-side of the study area. The dotted black line represents the orientation of the shore line in Noordwijk. for almost all the pixels (up to 0.8); with increasing wind, the RMSH diminishes (lower 340 roughness). For high wind speed most of the pixels show positive correlation with RMSH 341 (higher roughness).

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When considering the wind direction, see Figure 14, no significant correlation seems to 343 exist between wind speed and RMSH, except for a slightly more regular positive correlation 344 in the sectors ranging 90°-270°, where there also seems to be a more homogeneous behavior 345 for the 12 pixels of the area when considering specific wind direction. For other directions, 346 the correlation value is very variable for each considered pixel.

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The RMSH values have been now compared with PLS intensity and their correlation 348 has been evaluated for low, medium and high wind speed (See Figure 15). Excluding a 349 few cases of high wind conditions for certain pixels, in particular pixels located on the 350 city-side of the study area, a interesting positive correlation exists between PLS intensity 351 and RMSH for each wind speed in all the pixels. In particular, for low wind condition the 352 correlation is always positive; the cases of negative correlation are limited to a few pixels 353 and to medium-high wind conditions.

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The following analysis shows the comparison between SAR signal (VV polarization) 355 and RMSH index for each pixel (See Figure 16). In this analysis, no particular trend can be 356 highlighted in the correlation between SAR and RMSH, which is in general low and very 357 variable considering different pixels.

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As presented in Section 4, when environmental variables are not considered, SAR and 360 PLS data seems to have a low correlation (see Figure 8). When considering wind speed in 361 the evaluation of SAR backscatter and PLS intensity correlation, a positive correlation is 362 noticed only for low and medium wind speed conditions; for stronger wind, no correlation 363 can be noticed (see Figure 9). The PLS has a negative correlation with low and medium 364 wind speed; for high wind speed the correlation is high and always positive for each pixel 365 (see Figure 11). This phenomenon could be explained with the following hypothesis: High wind speed could dry the sand and, as a consequence, the PLS intensity is higher 367 (since low sand moisture values correspond to higher PLS intensity [10,15]); Correlation factor (colorbar) between RMSH and wind speed evaluated for different overlapping sectors ranging 90°wind directions. In the figure, each sector represents a 90°wind direction section and each of the 12 rings represents a row of pixel starting from pixel 1, which is located on the sea-side (inner ring) and moving towards pixel 12 (external ring), which is located on the city-side of the study area. The dotted black line represents the orientation of the shore line in Noordwijk. PLS intensity. In fact, the activation of aeolian transport requires wind speed above 371 certain values [53].

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The low correlation between SAR backscatter and PLS intensity for high wind speed can be 373 ascribed to the correlation trend between PLS intensity and wind: when PLS has a negative 374 correlation with wind speed (low and medium conditions), the behavior of its intensity is 375 similar to the SAR backscatter; for high wind speed, PLS intensity behavior is reversed and 376 it can no longer be compared to the SAR backscatter (compare Figures 9 and 11).

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RMSH seems to have negative correlation with wind speed only for low wind condition: 378 in this case, the effect of the wind is a reduction of the RMSH. For higher wind values, in 379 particular for 4-8 m/s, no correlation can be noticed, see Figure 13. The hypothesis is that 380 this phenomenon happens because wind speed in that range could produce a smoother 381 profile on the sand surface.

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Even if each pixel has a different correlation value, a positive correlation exists between 383 RMSH and PLS intensity, in particular for low/medium wind speed (see Figure 15), whilst 384 the correlation between SAR backscatter and RMSH is low but generally positive (see 385 Figure 16). The hypothesis in this case is that this can be related to the order of magnitude 386 of the RMSH values evaluated in the present work, which might not significantly affect 387 the SAR wavelenght. For future studies, direction/orientation of the roughness, could be 388 considered for determining a correlations with SAR data, as well as SAR systems with 389 higher resolution with respect to Sentinel-1 which can be used and correlated to RMSH 390 evaluated on different window size; roughness indices can be also evaluated on a lower 391 order of magnitude to identify more specific correlations.

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The correlation between PLS intensity and SAR backscatter shows specific wind 393 directions where the correlation is particularly relevant. The same occurs for the correlation 394 between PLS intensity and wind speed. The correlation between PLS intensity and wind 395 speed, for low and medium wind speed, is negative; correlation between SAR backscatter 396 and PLS intensity exists only when the correlation between PLS intensity and wind speed 397 is negative. The wind direction where the correlation between PLS and wind speed is 398 minimum (South) is the same than the direction where the correlation between SAR and 399 PLS is maximum. South is also the direction where low and medium winds generally come 400 from (compare Figures 3, 10 and 12).

402
An investigation of the correlation between a permanently installed TLS and SAR 403 systems has been conducted on the beach of Noordwijk: TLS data have been compared 404 with simultaneously acquired Sentinel-1 SAR images. The correlation between TLS and 405 SAR systems on sandy environments and the effect of environmental variables on their 406 correlation have been analyzed for the first time. The wind both in terms of wind speed 407 and direction has an impact on the correlation which could be further investigated, as well 408 as the roughness which -at the scale used in the present work -did not show significant 409 result but can be further analyzed on different scales to highlight more detailed information. 410 The study showed that the correlation between the two considered systems when not 411 considering external variables is positive but low (up to 0.25). When considering the wind 412 speed, a higher correlation between TLS and SAR (up to 0.5) exists in the case of low and 413 medium wind speed, whilst no particular correlation could be highlighted for high wind 414 speed condition; a dependence on the considered pixel location of the study area has been 415 noticed.

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The wind direction has also been considered: for directions ranging 90°-270°, the entire 417 area is homogeneous and there is a positive correlation between TLS and SAR up to 0.6, 418 whilst for directions ranging 210°-360°, the correlation is negative up to 0.4. The correlation 419 between TLS and wind has been separately considered with the following results: for 420 low and medium wind, PLS and wind speed have a negative correlation whilst for high 421 wind speed the correlation turns positive and ranges between 0.6 and 0.8. The correlation 422 between TLS and wind speed also depends on the wind direction: for directions ranging 423 90°-300°a negative correlation is showed and for directions 210°-360°there is a positive 424 correlation.

425
The influence of the surface roughness -evaluated in terms of RMSH -variable has 426 been also considered, at first in terms of correlation between RMSH and wind. For low 427 wind speed condition, the correlation between RMSH and wind is negative up to 0.8; 428 the correlation gets positive (higher roughness) with the increase of the wind speed. No 429 interesting correlation has been highlighted when considering the wind directions.

430
The analysis of the correlation between PLS and RMSH showed a positive correlation 431 for each wind speed. In the analysis of the correlation between SAR and RMSH instead, 432 no particular trend has been highlighted. In conclusion, this preliminary study allowed 433 the individuation of a first range of conditions where TLS and SAR data present a good 434 correlation. A better knowledge of the scenarios where the correlation between TLS and 435 SAR is applicable, and of the extent of the existing correlation, could allow the exploitation 436 of the combined use of TLS and SAR advantages, moving from the small scale (TLS) to a 437 world-wide scale (SAR).

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Author Contributions: The analysis has been conceived and designed by the three authors. VDB and 439 MK collected the data and contributed data and analysis tools. VD performed the analysis presented 440 in the results and wrote the paper. MK